Exam 4 Review Math1314
Evaluate the function at the given value of x. Round to 4 decimal places if necessary.
1x
1) f (x) = ; f (-5)
3
Graph the function and write the domain and range in interval notation.
2) f (x) = 4x
Solve the problem.
3) Suppose $8000 is invested with 3.5% interest for 3 yr under the following compounding options.
Complete the table.
Compounding Option n Value
Result
a. Annually
b. Continuously
Write the equation in exponential form.
4)
log3 243 = b
Write the equation in logarithmic form.
3
5) 8 = b
Write the equation in exponential form.
1
6) log 7 = 49
2
Write the equation in logarithmic form.
3
7) 10 = 1000
Simplify the expression.
1
8) ln 6
e
Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if
possible.
9) log 64x
8
1
Use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then
simplify if possible.
e
10) ln
18
Apply the power property of logarithms.
11) ln
5 9
x
Write as the sum or difference of logarithms and fully simplify, if possible. Assume the variable
represents a positive real number.
4
12) log ab
c8
Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
9
8
3x(x - 4)
13) ln 7
9 - 2x
Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as
possible.
14) log 180 - log 20
3
3
15) log x - 3log y
7
7
16)
- 2log7 z
1
log p + 3log7 2
2 7
Solve the problem.
17) Given that log 3 ≈ 0.4771 and log 8 ≈ 0.9031, use the properties of logarithms to approximate the
following. Do not use a calculator.
3
log 64
Use the change-of-base and a calculator to approximate the logarithm to 4 decimal places.
18) log 13
4
Solve the equation.
x+4
19) 32
= 26x
2
(4x - 4)
20) 7
= 1 (x - 7)
49
Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4
decimal places if necessary.
21) 24 log (3p - 77) = 48
4
Solve the logarithmic equation.
22) log x = 1 - log(x + 3)
Solve the equation.
23) log t + log (t + 2) = log 35
7
7
7
Find an equation for the inverse function.
24) f (x) = ln(x + 9)
Determine whether the ordered pair is a solution of the system.
2
25)
, 8 ;
9
9x + 8y = 66
-27x - 4y = -41
A system of equations is given in which each question is written in slope-intercept form. Determine the
number of solutions. If the system does not have one unique solution, state whether the system is
inconsistent or whether the equations are dependent.
2
26) y = x - 6
5
2
y = x - 8
5
Solve the system by substitution.
15x - y = 5
27)
25x + 4y = -3
Solve the system of equations by using the addition method.
28) 5x - 3y = -19
4x + 5y = 7
3
a. Graph the equations in the system.
b. Solve the system by using the substitution method.
29) y = x2 - 4
y = 2x - 4
Solve the system of equations by using the addition method.
30) 4x2 + 3y2 = 19
x2 + 4y2 = 8
Solve the system.
31) x2 + y2 = 10
3y2 - x2 = 14
Evaluate the determinant of the given matrix.
5
6
5
32) A = 7
25 35
ex e8x
33) A = 3 -e7x
Evaluate the determinant of the given matrix and state whether the matrix is invertible.
-7 -4 7
34) A = [aij] = 3 -6 7
5 -7 -2
For what values of x, y, and z will A = B?
-3 x
y -1
35) A = B = z -6
-8 -6
Find B - A.
-5 3
5 5
36) A = 4 -3 , B = 9 1
8 -8
3 9
4
Perform the indicated operations.
37) Find 5A
-2 0 1
1
A = -1 2 5
Given the matrices A and B, solve for X.
38) 4X - B = A.
A = -5 -3
2 -1
and B = -1 -4
5 -4
5
Answer Key
Testname: 1314 EXAM4 REVIEW
1)
243
2)
y
10
-5
5
x
Domain: (-∞, ∞)
Range: (0, ∞)
3)
Compounding Option n Value Result
a. Annually
1
$8869.74
b. Continuously
n/a $8885.68
b
4)
3 = 243
5)
log8 b = 3
491/2 = 7
7) log 1000 = 3
8) -6
9) 2 + log x
8
6)
10) 1 - ln(18)
11)
9
ln x
5
12)
1
1
log a + log b - 8log c
4
4
1
9
13) ln 3 + ln x + 8ln (x - 4) - ln (9- 2x)
7
14) 2
x
15) log 3 2
7 y z
16) log (8
7
p)
17) -1.3291
6
Answer Key
Testname: 1314 EXAM4 REVIEW
18) 1.8502
19) {20}
20) 3
21) {31}
22) {2}
23) {5}
24) -1
f (x) = ex - 9
25) No
26) No solution; The system is inconsistent.
1
27)
, -2
5
28) {(-2, 3)}
29) {(0, -4), (2, 0)}
6 y
5
4
3
2
1
-5 -4 -3 -2 -1
-1
1
2
3
4
5x
-2
-3
-4
-5
-6
30) {(2, 1), (2, -1), (-2, 1), (-2, -1)}
31) {(2, 6), (2, - 6), (-2, 6), (-2, - 6)}
32) -5
8x
33) -4e
34) -528, Yes
35) x = -1, y = -3, z = -8
10 2
5 4
-5 17
-10 0 5
37)
-5 5 2 1
36)
7
Answer Key
Testname: 1314 EXAM4 REVIEW
3
- - 1
4
38)
1 - 2
8